Monkey I'm with that is eating rubbish (7)
I believe the answer is:
imitate
'monkey' is the definition.
(thesaurus)
'i'm with that is eating rubbish' is the wordplay.
'with' is a charade indicator (letters next to each other).
'that is' becomes 'ie' ('i.e.' can be a synonym of 'that is').
'eating' indicates putting letters inside.
'rubbish' becomes 'tat' (I've seen this before**).
'ie' going around 'tat' is 'itate'.
'im'+'itate'='IMITATE'
(Other definitions for imitate that I've seen before include "Parrot" , "Take as a model" , "Copy (mannerisms)" , "Copy, simulate" , "I ate Tim! (anag.)" .)